Agentic AI deployments face a recurring design tension: heavy human oversight limits scale, while broad autonomy outruns accountability. Neither posture provides the governance infrastructure required for responsible delegation. We present the Digital Apprentice, a framework for scalable, safe AI agency in which autonomy is earned, not assumed. The Digital Apprentice is a developmental learner that internalizes the tacit methodology of a directing human, graduating through per-skill autonomy tiers only when empirical evidence justifies it. The result is an agent that becomes genuinely useful over time while remaining aligned to a specific human's standards. Three architectural components make this possible. (1) Methodology capture, distilling a directing professional's tacit approach into structured assets. (2) Authorization, with autonomy escalation gated by explicit human approval. (3) Continuous alignment, correcting drift at runtime and converting each correction into owned preference data. We instantiate this framework as an inference-time control plane. We mathematically model the quality framework and discuss policies and techniques designed to raise quality. We apply the framework to an open professional corpus, and we show how catching data drift and applying a different technique at runtime recovers degraded quality dimensions under traffic shift. The implication extends beyond any single application. We believe these three pillars, stitched together as a system, form a safer and more viable path to agentic systems that can scale without sacrificing trust.